**The Basic Concepts of Expression and Equations**

In algebra, letters are used as variables. A **variable** can assume values of numbers. Numbers are called **constants** .

**Math Note:** In some cases, a letter may represent a specific constant. As you will see in Chapter 9 , the Greek letter pi (π) represents a constant.

An **algebraic expression** consists of variables, constants, operation signs, and grouping symbols. In the algebraic expression 3x, the "3" is a constant and the "x" is a variable. When no sign is written between a number and a variable or between two or more variables, it means multiplication. Hence the expression "3x" means "3 times x or to multiply 3 by the value of x. The expression abc means a times b times c or a × b × c.

The number before the variable is called the **numerical coefficient** . In the algebraic expression "3x", the 3 is the numerical coefficient. When the numerical coefficient is 1, it is usually not written and vice versa. Hence, xy means 1xy. Likewise, 1xy is usually written as xy. Also –xy means –1xy.

An algebraic expression consists of one or more **terms** . A **term** is a number or variable, or a product or a quotient of numbers and variables. Terms are connected by + or – signs. For example, the expression 3x + 2y – 6 has 3 terms. The expression 8p + 2q has two terms, and the expression 6x ^{2} y consists of one term.

**Evaluating Algebraic Expressions**

*In order to* *evaluate**an algebraic expression, substitute the values of the variables in the expression and simplify using the order of operations* .

**Examples**

**Example 1**

Evaluate 2xy when x = 2 and y = 5.

**Solution 1**

2xy = 2(2)(5)

= 20

Hence, when x = 2 and y = 5, the value of the expression 2xy is 20.

**Example 2**

Evaluate –3x ^{2} when x = 6

**Solution 2**

**Example 3**

Evaluate 5(x + 3y) when x = –5 and y = 3.

**Solution 3**

**Evaluating Algebraic Expressions Practice Problems**

**Practice**

Evaluate each of the following expressions:

1. 17 – x when x = 7

2. x + 2y when x = –5 and y = 8

3. (2x + 5) ^{2} when x = 6

4. 3x – 2y + z when x = –3, y = 4, and z = 3

5. 5x ^{2} – 2y ^{2} when x = 3 and y = 6

**Answers**

1. 10

2. 11

3. 289

4. –14

5. –27

Practice problems for this concept can be found at: Expressions And Equations Practice Test.

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